arXiv preprints from January 1, 2026 through September 21, 2026 — 03:44:57 EST
This work addresses a longstanding gap in the statistical foundations of marginal maximum likelihood estimation for high-dimensional latent variable models. Marginal maximum likelihood estimation is widely used to fit latent variable models across the social sciences, ecology, and machine learning. Despite its broad use, rigorous...
Parameter estimation in finite mixture models can exhibit highly heterogeneous convergence behavior: locally isolated components may be estimated substantially faster than groups of competing components. Existing analyses based on Wasserstein distances typically characterize only the worst-case rate and therefore do not fully capture...
Neural PDE solvers provide efficient surrogates for time-dependent physical systems, but autoregressive prediction over long horizons remains challenging because local errors can induce distribution shift and accumulate under recursive deployment. We develop a variational approach to this problem by introducing latent Markov dynamics...
Model robustness analysis estimates an effect across a multiverse of specifications that pools control sets identifying the declared estimand with sets that condition on mediators or colliders. We propose stating rival assumptions about contested controls as a small set of candidate causal graphs, enumerating the adjustment sets each...
Causal discovery methods aim to determine the causal direction between variables using observational data. Functional causal discovery methods rely on structural and distributional assumptions to determine directionality but typically lack statistical inference. This paper reviews the statistical guarantees of existing functional...
Reserving models increasingly rely on loss-based estimation, where the loss function encodes the assumed error structure. Mack demonstrated this for the chain ladder, showing that the volume-weighted average estimator minimises a volume-weighted squared-error loss function that is additive in successive claim developments. This paper...
The chain ladder's volume-weighted pattern minimises an explicit loss function, yet is rarely booked as such. Practitioners adjust the pattern and record the final adjusted ratios. This paper treats the chain ladder's pattern selection as a supervised-learning problem. Judgement on pattern adjustments becomes a framework of defined...
Single-cell perturbation experiments provide causal information on gene regulation, whereas population-scale single-cell studies characterize gene expression and phenotypes in human populations. We develop a framework that integrates these complementary data sources for causal path analysis. Rather than assuming that a perturbational...
Anthropogenic forcing components follow different long-run paths, while persistent temperature change can involve distributional changes beyond the mean. Scalar regressions aggregate these components and retain only mean temperature, obscuring how distinct forcing paths relate to persistent distributional change. We develop new...
Local inference for spatial point distributions is dominated by Monte Carlo calibration. We develop an alternative based on the Tweedie--Miyasawa identities of empirical Bayes, which relate locally weighted moments of a point distribution under a Gaussian kernel to derivatives of its log-intensity in scale space. We first establish a...
Neighborhoods are multifaceted entities whose attributes span sociocultural, economic, and environmental dimensions. Clustering neighborhoods based on social determinants of health (SDoH) can inform the allocation of public health resources and interventions tailored to community needs. Continuous and bounded data, as seen in...
We develop a certified continuation framework for equilibrium computation and for training deep equilibrium networks (DEQs), with training formulated as interpolation to accuracy $2^{-b}$. For inference, compact input homotopy selects a unique branch from a supplied start root, and a rounded Newton tracker follows it under certified...
Contrail cirrus represents a critical component of aviation's non-CO2 climate impact, but its net radiative forcing, the balance between longwave warming and shortwave cooling, remains poorly constrained by direct observations. As a result, current assessments rely almost exclusively on microphysical models such as CoCiP and global...
Classification and regression trees are typically constructed using a greedy splitting rule that maximizes the immediate reduction in prediction error at each node. Although this strategy is computationally efficient, it can miss splits that yield small short-term gains but create substantial downstream improvements after further...
The purpose of this paper is the identification of high-fidelity digital twin data models from numerical code outputs by non-intrusive techniques (i.e., not requiring Galerkin projection of the governing equations onto the reduced modes basis). In this paper the author defines the concept of the digital twin data model (DTM) as a...
This paper develops an embedded-hybridized discontinuous Galerkin (E-HDG) method combined with a first-order implicit-explicit scalar auxiliary variable (IMEX-SAV) time discretization for variational initial-state data assimilation governed by the unsteady incompressible Navier-Stokes equations. We adopt an optimize-then-discretize...
We prove the generalized Cartan-Hadamard conjecture, also known as the Aubin conjecture, in the small volume regime under a lower Ricci curvature bound, for any dimension $n\geq 2$. More precisely, we show that if $(M^n,g)$ is a Cartan-Hadamard manifold satisfying $\mathrm{Sec}_g\leq\bar k\leq 0$ and $\mathrm{Ric}_g\geq...
The choice of Riemannian metric can strongly influence the convergence of gradient-based optimization over covariance matrices. Euclidean, Bures-Wasserstein and affine-invariant metrics are common choices, but their relative effectiveness depends on the objective. We introduce a two-parameter family defined by...
If ZFC is consistent, then so is ZF+DC+BPI+there is no Vitali set.
We continue to develop a theory of Besov and Triebel-Lizorkin spaces associated with weighted subcoercive operators on a real connected Lie group, specializing to the case of groups with polynomial volume growth. We consider the full scale of spaces and consider equivalent definitions, inclusions, discretization, and duality.
In the present paper, we study the maximization problem of the $k$-Torsional rigidity under quermassintegral constraint, with particular emphasis on the role of the ball. Our main result shows a phenomenon which, as far as we know, has not previously been observed: the ball, rather than being an extremal shape, is a saddle point. More...
The purpose of this paper is to extend an article by Hilhorst, Mimura and Sch{ä}tzle [18] about the limit as the latent heat coefficient tends to zero of a two-phase Stefan problem arising in biology. We introduce a rather general additive noise white in time and colored in space, and search for the limit of the solution of the...
We study complete stable minimal hypersurfaces in Riemannian manifolds under various curvature assumptions. In an $(n+1)$-dimensional complete oriented manifold with nonnegative scalar curvature, we prove that no complete oriented noncompact stable minimal hypersurface can be conformally equivalent to a bounded domain in an...
We study the problem of minimizing a weighted sum of squared Wasserstein distances with signed coefficients. In the case of a single positive coefficient, we derive two convex dual formulations: one expressed in terms of Brenier potentials, and one as a projection problem in convex order. Such dual formulations arise via Toland...
We classify finite-energy positive solutions to the Yamabe-type equation on the 15-dimensional octonionic Heisenberg group, whose algebra is non-associative. Extremals for the Folland-Stein-Sobolev inequality on this group are explicitly described. This confirms the conjecture of Garofalo and Vassilev [Duke Math. J. 2001] on the $15$...